Question: Simplify to lowest terms. $\dfrac{24}{36}$
Explanation: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 24 and 36? $24 = 2\cdot2\cdot2\cdot3$ $36 = 2\cdot2\cdot3\cdot3$ $\mbox{GCD}(24, 36) = 2\cdot2\cdot3 = 12$ $\dfrac{24}{36} = \dfrac{2 \cdot 12}{ 3\cdot 12}$ $\hphantom{\dfrac{24}{36}} = \dfrac{2}{3} \cdot \dfrac{12}{12}$ $\hphantom{\dfrac{24}{36}} = \dfrac{2}{3} \cdot 1$ $\hphantom{\dfrac{24}{36}} = \dfrac{2}{3}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{24}{36}= \dfrac{2\cdot12}{2\cdot18}= \dfrac{2\cdot 2\cdot6}{2\cdot 2\cdot9}= \dfrac{2\cdot 2\cdot 3\cdot2}{2\cdot 2\cdot 3\cdot3}= \dfrac{2}{3}$